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4/10/2011
1
•
Integration
•
Trapezoidal rule
•
Riemann’sintegral
Lecture 18: Numerical integration
•
Simpson’s rule
•
Matlab built in functions for integration
•
Error analysis
Integration
For a function
f
,
The “integral of
f
from
a
to
b
” is the area under the graph of the
function.
If f is continuous, then the area is well defined, as the common
limit of upper and lower sums.
The integral is denoted
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2
If a function g is the primitive of
f
, namely
Integration
x
f
x
g
for all
x
, then the fundamental theorem of calculus gives that the
integral of
f
can be computed by evaluating
g
But finding primitives can be hard…
)
(
)
(
)
(
a
g
b
g
dx
x
f
b
a
In many cases of engineering and scientific (and economics, etc)
interest
–
the functions do not have known primitives, so…
–
the integral (area) must be approximated by a finite
number of function evaluations.
Discretization grid
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This note was uploaded on 09/07/2011 for the course ENGIN 7 taught by Professor Horowitz during the Spring '08 term at University of California, Berkeley.
 Spring '08
 HOROWITZ

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